Gorenstein spherical Fano varieties

被引:14
|
作者
Gagliardi, Giuliano [1 ]
Hofscheier, Johannes [1 ]
机构
[1] Univ Tubingen, Fachbereich Math, D-72076 Tubingen, Germany
关键词
Spherical varieties; Fano varieties; Lattice polytopes;
D O I
10.1007/s10711-015-0047-y
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We obtain a combinatorial description of Gorenstein spherical Fano varieties in terms of certain polytopes, generalizing the combinatorial description of Gorenstein toric Fano varieties by reflexive polytopes and its extension to Gorenstein horospherical Fano varieties due to Pasquier. Using this description, we show that the rank of the Picard group of an arbitrary -dimensional -factorial Gorenstein spherical Fano variety is bounded by . This paper also contains an overview of the description of the natural representative of the anticanonical divisor class of a spherical variety due to Brion.
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页码:111 / 133
页数:23
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